His advisor's memoir is also interesting:

"So after Yitang graduated, I told him the normal way of seeking jobs. When I looked into his eyes, I found a disturbing soul, a burning bush, an explorer who wanted to reach the north pole, a mountaineer who determined to scale Mt. Everest, and a traveler who would brave thunders and lightnings to reach his destination. Yitang never came back to me requesting recommendation letters. Apparently, he did not seek a job. Even to the date Yitang announced his monumental result I did not know what was the best for him. Though I was sure of one thing, − he could not survive the life of “tenure-track,” “tenure,” and “promotions”. It was not his type. I regarded him as a free spirit, and I should let him fly."

http://www.math.purdue.edu/~ttm/ZhangYt.pdf

Yitang Zhang is an outlier in that sense, like Alexander Grothendick and Grigori Perelman. Many other great mathematicians, like Terence Tao, Timothy Gowers, etc. and even some working on 'big problems' like Andrew Wiles are in stable academic jobs. If his own words [1] are anything to go by, Zhang's situation is probably due to his adviser's unwillingness or inability to recommend him for good academic positions.

[1] http://nautil.us/issue/5/fame/the-twin-prime-hero

The article that got to me first was from ABC news (http://abcnews.go.com/US/wireStory/2014-macarthur-genius-gra...).

Making only a sidenote that the group of recipients includes a mathematician, they also say "Most winners are not widely known outside their fields ..." I thought Zhang deserves a bit more recognition than this, especially since his rise from "relative obscurity" is pretty unique.

Its not so much about the solution being useful, its more about finding out if the solution exists. Its sort of a self challenge, like a mental marathon. Generally speaking there isn't much need for you to run 26 miles, let alone do it very fast.

But you do it, for the challenge, the learning, and to grow as a person. Because the finish line isn't why your running, your running because you like running.